On the search for variational principles

Abstract Several attempts to formulate variational principles for non-self-adjoint and nonlinear systems are examined. The variational formulations are found to lack the advantages of genuine variational principles, chiefly because the variational integral is not stationary or because no variational integral exists. The corresponding variational methods of approximation are shown to be equivalent to the more straightforward Galerkin method or another closely related version of method of weighted residuals. The methods due to Rosen (restricted variations), Glansdorff and Prigogine (local potential), and Biot (Lagrangian thermodynamics) are treated. It is concluded that there is no practical need for variational formulations of the sort examined.

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